arXiv subjects

Alexandros Tsolovikos

Publications and source records attributed to Alexandros Tsolovikos.

2 recordsLinked to original sources

arXiv2021

Nonlinear Covariance Steering using Variational Gaussian Process Predictive Models

In this work, we consider the problem of steering the first two moments of the uncertain state of an unknown discrete-time stochastic nonlinear system to a given terminal distribution in finite time. Toward that goal, first, a non-parametric predictive model is learned from a set of available training data points using stochastic variational Gaussian process regression: a powerful and scalable machine learning tool for learning distributions over arbitrary nonlinear functions. Second, we formulate a tractable nonlinear covariance steering algorithm that utilizes the Gaussian process predictive model to compute a feedback policy that will drive the distribution of the state of the system close to the goal distribution. In particular, we implement a greedy covariance steering control policy that linearizes at each time step the Gaussian process model around the latest predicted mean and covariance, solves the linear covariance steering control problem, and applies only the first control law. The state uncertainty under the latest feedback control policy is then propagated using the unscented transform with the learned Gaussian process predictive model and the algorithm proceeds to the next time step. Numerical simulations illustrating the main ideas of this paper are also presented.

math.OC↗

arXiv2020

Greedy Finite-Horizon Covariance Steering for Discrete-Time Stochastic Nonlinear Systems Based on the Unscented Transform

In this work, we consider the problem of steering the first two moments of the uncertain state of a discrete time nonlinear stochastic system to prescribed goal quantities at a given final time. In principle, the latter problem can be formulated as a density tracking problem, which seeks for a feedback policy that will keep the probability density function of the state of the system close, in terms of an appropriate metric, to the goal density. The solution to the latter infinite-dimensional problem can be, however, a complex and computationally expensive task. Instead, we propose a more tractable and intuitive approach which relies on a greedy control policy. The latter control policy is comprised of the first elements of the control policies that solve a sequence of corresponding linearized covariance steering problems. Each of these covariance steering problems relies only on information available about the state mean and state covariance at the current stage and can be formulated as a tractable (finite-dimensional) convex program. At each stage, the information on the state statistics is updated by computing approximations of the predicted state mean and covariance of the resulting closed-loop nonlinear system at the next stage by utilizing the (scaled) unscented transform. Numerical simulations that illustrate the key ideas of our approach are also presented.

math.OC↗